There are many systems for controlling the initiation and termination of communications between computer units or devices over a common bus. Some systems permit devices to initiate use of the bus solely during repeating time periods assigned to the respective devices. Some systems assign different priorities to different devices, and permit devices to initiate use of the bus in order of priority without waiting for an assigned time period. The prior arrangements involve an undersirably large amount of control equipment and procedures, such as may be included in and provided by a computer connected to the bus.